document.write( "Question 1186707: Find the constant C such that the denominator will divide evenly into the numerator.\r
\n" ); document.write( "\n" ); document.write( "x^4-x^3-3x^2-Cx-3/x-3\r
\n" ); document.write( "\n" ); document.write( "Show the solution. \n" ); document.write( "
Algebra.Com's Answer #817666 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Find the constant C such that the denominator will divides evenly into the numerator.
\n" ); document.write( "x^4-x^3-3x^2-Cx-3/x-3
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The linear binomial (x-3) in the denominator divides the polynomial  f(x) = x^4 - x^3 - 3x^2 - Cx - 3  of the numerator evenly \r\n" );
document.write( "\r\n" );
document.write( "if and only if  f(3) = 0   (the Remainder Theorem).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From condition  f(3) = 0  find the value of C\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3^4 - 3^3 - 3*3^2  - C*3 - 3 = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3C = 3^4 - 3^3 - 3*3^2 - 3 = 81 - 27 - 3*9 - 3 = 24.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  C = 24/3 = 8.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  f(3) = 3^4 - 3^3 - 3*3^2 - 8*3 - 3 = 81 - 27 - 27 - 24 - 3 = 0.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The response by @josgarithmetic,  giving the answer   \"highlight%28C=26%29\"   is  INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\\\\\\\\\\\\\\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After my noticing, @josgarithmetic fixed his erroneous answer,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "but his calculations (starting from the setup equation) remained INCORRECT.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "NEVER trust his solutions; ALWAYS avoid his posts, for your safety.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This person makes errors everywhere and always.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );